A New Subgraph of Minimum Weight Triangulations

Cao An Wang, Francis Chin and Yin-Feng Xu
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Cao An Wang: Memorial University of Newfoundland
Francis Chin: University of Hong Kong
Yin-Feng Xu: Xi‘an Jiaotong University

Journal of Combinatorial Optimization, 1997, vol. 1, issue 2, No 1, 115-127

Abstract: Abstract In this paper, two sufficient conditions for identifying a subgraph ofminimum weight triangulation of a planar point set are presented. Theseconditions are based on local geometric properties of an edge to beidentified. Unlike the previous known sufficient conditions for identifyingsubgraphs, such as Keil‘sβ-skeleton and Yang and Xu‘s double circles, The localgeometric requirement in our conditions is not necessary symmetric withrespect to the edge to be identified. The identified subgraph is differentfrom all the known subgraphs including the newly discovered subgraph:so-called the intersection of local-optimal triangulations by Dickerson etal. An O(n3) time algorithm for finding this subgraph from a set ofn points is presented.

Keywords: Mathematical Modeling; Industrial Mathematic; Geometric Property; Discrete Geometry; Time Algorithm (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1009796113861

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